Vibration isolation techniques are used to reduce the motion transmitted from a vibratory base to a device or system. The basic components are illustrated in FIG. 1. The device, represented by the rigid mass, m, is connected to the base with a linear spring and damper pair, k and c, respectively. The governing equation for this system is:m{umlaut over (x)}+c({dot over (x)}−{dot over (y)})+k(x−y)=0or{umlaut over (x)}+2ζωn({dot over (x)}−{dot over (y)})+ωn2(x−y)=0where 2ζωn=c/m and ωn2=k/m.
For practical purposes, transmissibility is defined as the ratio of the amplitude of the device motion (x) to that of the base motion (y). Assume that y(t) is sinusoidal of frequency ω. Some algebraic manipulation gives:
  TR  =            (                        1          +                                    (                              2                ⁢                ζβ                            )                        2                                                              (                              1                -                β                            )                        2                    +                                    (                              2                ⁢                ζβ                            )                        2                              )              1      /      2      where β=ω/ωn.
The damping ratio, ζ, is equal to 0.5 c/(mk)1/2. A plot of TR for various levels of the damping ratio, ζ, is shown in FIG. 2.
A passive mechanical spring-mass-damper system with external vibrational excitation is analogous to a passive electrical network consisting of resistors, capacitors and inductors that is excited by a voltage waveform. Both systems can be utilized as second order filters with the following Laplacian characteristic equation:s2+2sζωn+ωn2=0where ωn is the system natural frequency and ζ is the damping coefficient. Such systems can be utilized to spectrally pass, reject, or attenuate frequency components of the external forcing function's bandwidth, whether a voltage signal for an electrical filter or a vibrational waveform for a mechanical filter.
However, unlike electrical filters where the system components can be easily tunable, mechanical filter components are difficult to tune. As such, the filter characteristics (ωn and ζ) are difficult to adjust in mechanical filters (vibration filters). This is particularly complicated in micromachined or MEMS devices, which are usually fabricated in crystalline silicon, because it is difficult to obtain sufficient damping to prevent ringing. This is often accomplished by hermetically packaging the MEMS device in a fluid at a prescribed pressure, and tailoring the device design to utilize squeeze-film or sheer resistance damping. These techniques are both expensive to implement and limited in application. Without sufficient damping, mechanical devices will oscillate (ring) for an unacceptably long length of time when externally excited.
In macroscale devices, electromagnetic actuators (such as DC or AC motors) are far more efficient and practical than electrostatic actuators. However, as devices are shrunk to the micro level, electromagnetic forces shrink faster than electrostatic forces because electromagnetic forces tend to be proportional to volume while electrostatic forces tend to be proportional to area, for the same amount of applied energy. Therefore for micro (i.e. MEMS) devices, electrostatic forces tend to be stronger than electromagnetic forces. Hence, electrostatic actuators are often used in MEMS applications.
A commonly used MEMS electrostatic actuator is the comb drive actuator, which consists of two comb shaped structures aligned to interdigitate the comb teeth. One of the combs is spatially fixed, while the other one is allowed to move so that its interdigitated teeth can move into or out of the teeth of the fixed comb. When a voltage is applied across the two combs, the resulting electrostatic force is equal to:
      F    T    =            n      ⁢                          ⁢      β      ⁢                          ⁢      h      ⁢                          ⁢              ɛ        r            ⁢              ɛ        o            ⁢              V        2                    d      O      where FT is the tangential force pulling the combs together, n is the number of active teeth in the moveable comb, β is the fringe effect correction factor, h is the overlapping height between comb teeth, εrεo is the permittivity of the dielectric and dO is the fixed distance between a moveable comb tooth and a stationary comb tooth. Note that the force is proportional to the applied voltage squared, and is not proportional to the distance the movable comb has traveled.
Most comb drive actuators used to date in MEMS devices have been horizontally oriented, and usually implemented in silicon substrates. However, a vertical comb drive that moves the comb in or out of the plane of the silicon substrate in a particular MEMS micro mirror device application is known.
Tunable mechanical dynamic systems have been developed that are based around spring-mass-damper systems for a variety of applications. Typically, they consist of a mechanical system that serves some function that has at least one mechanical element that is tunable by moving a mechanical member with an actuator. Additionally, these systems employ a sensor of some kind to detect that the mechanical system needs tuning. Then a feedback mechanism is utilized to generate the actuation drive signal necessary to correct the error detected by the sensor. Often, the feedback mechanism is electronic and involves analog or digital signal processing. Examples include vibration sensing, vibration isolation, mechanically tuned electrical filters and MEMS tunable chaotic oscillators.
Some MEMS devices, such as many MEMS gyroscopic sensors, are extremely sensitive to and adversely affected by high frequency vibrations, which may be present in the environment in which the sensors are used. In order to use these kinds of devices in mechanically harsh environments, they must be protected from high frequency vibrations. This can be accomplished by fabricating a MEMS vibration filter and incorporating it into the sensor package to isolate the sensor die from high frequency vibrations. Passive MEMS vibration filters have been investigated for this purpose. Unfortunately, they lack tunability and suffer from excessive ringing due to the difficulties in obtaining sufficient mechanical damping in silicon based MEMS devices.
A MEMS spring-mass-damper mechanical system can be fabricated by micromachining silicon or some other material. A simple example of a MEMS system 10 is illustrated in FIG. 3. The system 10 consists of a frame 20, a proof mass 30 and four springs 40 that are fabricated out of the same material through MEMS fabrication processes, although they could be made from different materials. Damping (not shown) is provided through internal mechanical losses and/or external squeeze-film or sheer resistance methods. The springs 40 are designed to allow the proof mass 30 to move with respect to the frame 20 with one or more degrees of freedom, and may be of any shape. Additionally, the springs 40 are usually designed so that the proof mass 30 has much more mass than the spring structures. This structure has a second order low-pass frequency response, where the resonant frequency has been set by the proof mass and the system spring constant.
Problems with the type of system presented in FIG. 3 include the lack of a convenient way to obtain sufficient damping and the lack of tunability of the frequency response. What is needed is a micromachined device utilizing electrostatic actuators to filter vibrations caused by an external disturbance. What is also needed is a micromachined device having vertical comb drives to measure displacement between stationary and movable comb drive elements, and to generate a restoring force.